[palimpsests]

thanks and this isn't what I'm asking about, I'm aware of all of this (background in physics and in music performance).

of course people can hear and distinguish mathematically pure intervals especially if demonstrated in these ways.

you said,

> This brings some practical musical advantages, but even the average listener can hear the difference, the loss of purity of harmony

which I interpreted as meaning that average listeners are both hearing and actively aware of this difference in their day-to-day exposure to equal-tempered music.

I am very skeptical of this claim, but perhaps this is not what you intended to imply? I can understand why my question would lead to yours and geofft's answers.

[mhauru]

Ah, I see. Indeed, I did not mean to imply that the average listener is aware of the short-comings of equal temperament without somebody explicitly providing the contrasting example of just intonation. I merely meant to say that the difference between just intonation and 12-EDO is large enough that even an untrained ear can spot it, when e.g. the same chord is played in both tunings back-to-back. Something that probably wouldn't be the case if for instance all of the 12-EDO approximations would be as close to the just intonation interval as perfect fifths and fourths are.

I would hypothesise that even the average listener might enjoy some pieces of music somewhat more if they were played in just intonation (depends of course massively on the piece whether this is even realistic or a good idea, but given a suitable piece), but I doubt they would be concious of what's making the difference. Not saying I have any evidence of this, but that's my guesstimate of what the answer to the question "how much of a difference would just intonation vs 12-EDO make for the average listener" would look like.